How long really depends on the rabbit, some take to it within a couple days while others can take months. Generally rabbits who are spayed or neutered are easier to litter train, but intact rabbits can be trained as well. Young rabbits can also be harder to train as they usually don't have full control over when and where the pee and poop, but you can work on it and hope they get better as they get a bit older.
If they are already using one area of the cage to pee and poop, put the litter box in that area. Hopefully your rabbits will start to use the box.
If they are not using one area, then you put the box in a corner. Sweep up the poops in the cage and put those in the box. If you can get some pee, soak that with paper towel and put it in the box. You will need to keep the cage clean, so don't use shavings or other litter in the cage, but a blanket or towel could be used. Keep spot cleaning the cage a couple times a day, spraying the used areas with white vinegar does help too. It can take a little while for the rabbits to understand to use the litter box, but most will use it eventually.
When you do move them to a larger cage, the litter habits could suffer for a bit. This is due to them wanting to make the area and theirs. Don't clean the litter box before you move them, you can spot clean but leave dirty litter in it. You will have to keep the new cage clean until they start to use the litter box normally.
